This paper discusses two "GeoGebra" applets, "Radical" and "Parabola," that are designed to strengthen the conceptual understanding of specific topics in algebra. The design and pedagogical basis of the applets are presented. The integration of the applets in teaching Grade 9 mathematics in a partner high school in…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

Technology permeates our daily lives; education has not been untouched. Liaw (2002) points out that "teachers, trainers, and instructional designers of computer-based or Web-based instruction would benefit by being more attentive to learners' perceptions toward Web-based environments." Reviewing the earlier research into student perceptions toward…

In an attempt to study the emerging questions about design of mathematical tasks that could support the solving of challenging problems, we designed two settings of interactive diagrams that share an example represented as an animation of multi-process motion but differ in their organizational functions. The interactive settings, each comprising…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

Even though computer games hold considerable potential for engaging and facilitating learning among today's children, the adoption of modern educational computer games is still meeting significant resistance in K-12 education. The purpose of this paper is to inform educators and instructional designers on factors affecting teachers' adoption of…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

In the Singapore primary school Mathematics curriculum, students are taught the model method that uses bar diagrams to visualize the problem structure in a given word problem. When these students progress to secondary school, they learn the algebraic way of solving word problems. Studies (e.g. Ng et al.) have shown that poor bridging of students…

Discussion of the use of virtual reality (VR) to help students learn highlights the use of VR with elementary algebra. Learning theory is examined, including knowledge construction; knowledge representation is discussed, including the symbol systems of algebra; and spatial algebra is described and illustrated. (34 references) (LRW)

The purpose of this research was to design several "small" and "interesting" computer programs which were acceptable and stimulating to the student, were controlled by the student rather than the teacher, and produced understanding of the knowledge to be learned. This report describes the assumptions made about interaction, motivation, and the…

Describes a study that investigated the differential effects of Computer Algebra Systems (CAS) and metacognitive training (META) on mathematical reasoning. Participants were 83 Israeli eighth-grade students. Results showed that CAS embedded within META significantly outperformed the META and CAS alone conditions, which in turn significantly…

Describes study of university students that investigated the effects of two direct instruction techniques in a computer-based algebra lesson: the cognitive routine (CR) and the Corrective Feedback Paradigm (CFP). Research design is explained, results are analyzed, and further research is suggested. (nine references) (LRW)

The Corrective Feedback Paradigm (CFP), a computer-based instruction model, addresses the problem of inefficient sequencing of items in a set to be learned by suggesting the use of an increasing ratio review schedule for presenting drill items. With this system, items answered correctly are either removed from the list entirely or replaced at the…

Discussion of involving teachers and students in the learning process focuses on an approach that combined microcomputers, video cassette recorders, and print materials to design a high school algebra class. Course design is explained, software and hardware are described, improvement in student motivation is reported, and costs are considered.…